A147701 Expansion of q^(1/4) * eta(q) * eta(q^2) * eta(q^5) * eta(q^20) / (eta(q^4) * eta(q^10)^3) in powers of q.

1, -1, -2, 1, 1, 0, 0, 3, 1, -3, -1, -1, -4, -1, 3, 1, 4, 6, -1, -4, 1, -5, -12, 1, 10, -1, 4, 18, 1, -14, -2, -7, -22, -2, 15, 2, 14, 33, -2, -22, 3, -20, -52, 3, 37, -3, 22, 71, 4, -51, -4, -29, -90, -4, 61, 4, 50, 121, -5, -83, 5, -67, -174, 6, 123, -6, 74, 231, 6, -162, -7, -99, -286, -8, 195, 8, 148, 376, -9, -254, 11, -191

Offset

0,3

Links

Table of n, a(n) for n=0..81.

Formula

Euler transform of period 20 sequence [ -1, -2, -1, -1, -2, -2, -1, -1, -1, 0, -1, -1, -1, -2, -2, -1, -1, -2, -1, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 20^(1/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A144724.

Example

1/q - q^3 - 2*q^7 + q^11 + q^15 + 3*q^27 + q^31 - 3*q^35 - q^39 + ...

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A) / (eta(x^4 + A) * eta(x^10 + A)^3), n))}

Crossrefs

Sequence in context: A185184 A378085 A292894 * A228348 A057516 A293015

Adjacent sequences: A147698 A147699 A147700 * A147702 A147703 A147704

Keyword

sign

Author

Michael Somos, Nov 10 2008

Status

approved